Disregard to human life and health isn’t limited to a fascist government though. As for the propaganda, I always took that at making fun of the military and their over the top commercials and other media.
I never compared it to the actual government.
There is too many different versions of starship troopers to have a meaningful conversation about the logistics of how they travel. But there are transport bugs capable of interstellar travel. The first one was located on Pluto, so they were already in our system. Depending on which version of Starship Troopers you bring up Buenos Aires was either attacked directly by the bugs or had a meteor destroy it.
And the bugs have to have some sort of FTL travel since the humans followed the first transport bug back to the Arachnid homeworld. If that would take billions of years then the humans wouldn’t have been able to follow them back after they left Sol.
Starship Troopers is full of plot holes and inconsistencies that would, again, likely prevent us from having a meaningful conversation about the logistics of the Arachnids.